This book is addressed to researchers in mathematics education. It presents examples of application of a restricted number of theories in the design
and/or study of mathematics teaching situations. It shows how these the-
ories work in the practice of research. Without taking into account this
'second order' perspective, the articles may appear as telling banal sto-
ries and drawing banal conclusions. The theories reveal that the everyday
banality of the mathematics classroom situations is fraught with deep, un-
resolved didactic problems. They show that these problems will never be
solved if we continue to consider these situations as banal.